High-Resolution Rotational Spectroscopy in a Cold Ion Trap: ${\mathrm{H}}_2{\mathrm{D}}^{+}$ and ${\mathrm{D}}_2{\mathrm{H}}^{+}$

The lowest-lying $1_{01}\leftarrow 0_{00}$ transition of $para\mathrm{\text{−}}{\mathrm{H}}_2{\mathrm{D}}^{+}$ and $1_{11}\leftarrow 0_{00}$ of $ortho\mathrm{\text{−}}{\mathrm{D}}_2{\mathrm{H}}^{+}$ has been detected by the enhancement of the $\mathrm{D}/\mathrm{H}$ isotope exchange reaction in collisions with $p\mathrm{\text{−}}{\mathrm{H}}_2$ upon rotational excitation. These are the first pure rotational spectra of molecular ions by action spectroscopy. For this purpose, a cryogenic multipole ion trap has been combined with narrow-band tunable radiation sources operating in the 1.25 to 1.53 THz range. The low temperature of the ions allows us to determine the astronomically important transitions with a relative precision of $\Delta \nu /\nu ={10}^{-8}$. While the 1 476 605.708(15) MHz line center frequency for the $o\mathrm{\text{−}}{\mathrm{D}}_2{\mathrm{H}}^{+}$ transition agrees very well with previous unpublished work, the 1 370 084.880(20) MHz line center frequency for the $p\mathrm{\text{−}}{\mathrm{H}}_2{\mathrm{D}}^{+}$ transition deviates by 61 MHz. Potential future applications of this new approach to rotational spectroscopy are discussed.

Figure 1

Experimental setup consisting of the ion trapping machine and the THz source. The unit consisting of THz source and elliptical mirror (on the right) is placed on a common support, which can be moved between the trapping machine and a test setup on a nearby optical bench (not shown). In both setups, a HeNe laser defines the beam path, to which the THz source is adjusted by a $xyz$-stage.

Figure 2

Action spectrum of the ${\mathrm{H}}_2{\mathrm{D}}^{+}$ rotational transition $1_{01}\leftarrow 0_{00}$, observed as a decrease of the ${\mathrm{H}}_2{\mathrm{D}}^{+}$ parent species and as an increase of the product ion counts ${\mathrm{H}}_3^{+}$ when the excitation frequency is in resonance. The baseline of background counts of a few hundred ions has been subtracted in both cases and only relative ion count changes are shown. Both traces have been recorded under different experimental conditions. The ${\mathrm{H}}_2{\mathrm{D}}^{+}$ trace has been obtained at a higher $p\mathrm{\text{−}}{\mathrm{H}}_2$ number density of about $4\times {10}^{11}{\mathrm{cm}}^{-3}$. The Doppler width of ${\sigma }_{\mathrm{D}}\approx 1\mathrm{MHz}$ corresponds to a kinetic ion temperature of 23 K.

Figure 3

The rotational transition $1_{11}\leftarrow 0_{00}$ of ${\mathrm{D}}_2{\mathrm{H}}^{+}$ has been detected by counting the number of parent ions (${\mathrm{D}}_2{\mathrm{H}}^{+}$) or product ions (${\mathrm{H}}_3^{+}$ and ${\mathrm{H}}_2{\mathrm{D}}^{+}$) after a trapping time of 870 ms. The ${\mathrm{H}}_3^{+}$ and ${\mathrm{H}}_2{\mathrm{D}}^{+}$ traces were recorded under similar experimental conditions, showing that reaction to ${\mathrm{H}}_2{\mathrm{D}}^{+}$ is more probable than ${\mathrm{H}}_3^{+}$, while the ${\mathrm{D}}_2{\mathrm{H}}^{+}$ trace has been recorded at a $p\mathrm{\text{−}}{\mathrm{H}}_2$ number density of about $5\times {10}^{11}{\mathrm{cm}}^{-3}$. The Doppler width of this signal is ${\sigma }_{\mathrm{D}}\approx 1\mathrm{MHz}$, yielding an ion temperature of about 25 K. Applying small frequency steps of 72 kHz and sufficient iterations, the center frequency of the ${\mathrm{D}}_2{\mathrm{H}}^{+}$ trace is obtained with an accuracy of 15 kHz, see Table .